How does this work out?

Test Preparation SAT Preparation
1

<p>I am getting the hard math q's right but these are tripping me. Isn't a normal coin two-sided? Therefore if you flip a quarter 3 times, probablilty is: 1/2...1/2...1/2. So i did .5*.5 but its not right!</p>

<p>A two-sided coin is tossed three times. What is the probability that 'heads' will be the result exactly two times?</p>

<p>A) 3/4</p>

<p>B) 2/3</p>

<p>C)1/2</p>

<p>D) 3/8</p>

<p>E)1/4</p>

<p>Answer: "And they call this a tough one... You've got 2 possible outcomes for each throw, so 8 total. That's your denominator. How many of them meet your criteria? Write them out: HHT, HTH, or THH. 3 out of 8. or 3/8 is your answer."</p>

2

<p>.5*.5 is the probability that you will get them in that particular order (i.e. HHT), there are 3 different permutations with 2 heads so you need to take them all into account.</p>

3

<p>For a question with only 3 tosses, you might want to use a tree diagram (instead of a formula) - dots are for spacing only:</p>

<p>Toss #1:..........H.....................................T
Toss #2:.....H........T..........................H...........T
Toss #3:...H...T...H...T....................H....T......H....T</p>

<p>Then simply follow each of the 8 branches to see how many have two heads.</p>

<p>Sometimes tree diagrams aren't the most time-efficient way to solve a problem, but for only 3 tosses, it doesn't suck.</p>

4

<p>Firstly, it would be (1/2)^3 for the chance of one permutation, not (1/2)^2.</p>

<p>Then it is matter of considering the different permutations, as fhg said, and multipling them by the chance of one.</p>

<p>In this case, (1/2)^3 = 1/8</p>

<p>1/8 * 3 = 3/8</p>

<p>Answer is 'D'.</p>